Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Main {

    static final long M = 1000000007;

    public static void main(String args[]) {

        FastReader io = new FastReader();

        int n = io.nextInt();

        if(n%2 == 0){
            System.out.println(n/2 + 1);

            for(int i = 1;i <= n/2;i ++){
                System.out.println(i + " " + i);
                System.out.println(i + " " + (i + 1));
            }
        }
        else{
            System.out.println((n - 1)/2 + 1);

            for(int i = 1;i <= (n-1)/2 + 1;i ++){
                System.out.println(i + " " + i);
                if(i < (n - 1)/2 + 1){
                    System.out.println(i + " " + (i + 1));
                }
            }
        }

    }
}

 class Solver{
    static final long MAX = 10000000000L;
    public void solve(){


    }
 }

 class Util{
    static  final  long M = 1000000007;
    static long modexp(long n,long m){
        if(m==0)
              return 1;
        else if(m==1)
            return n;
        else{
            long p = modexp(n,m/2);

            if(m%2==1)
                return (((p*p)%M)*n)%M;
            else
                return (p*p)%M;
        }
    }

    static  long exp(long n,long m){
        if(m == 0)
            return 1;
        if(m == 1)
            return n;

        long p = exp(n,m/2);

        if(m%2 == 1)
            return p*p*n;
        else
            return p*p;
    }

    static long gcd(long a,long b){
        if(a==0)
            return b;

        return gcd(b%a,a);
    }

    static long inv(long n){
        return modexp(n,M-2);
    }

    static long lcm(long a,long b){
        return a*b/gcd(a,b);
    }
    static long factorial(long fact[],long n){
        fact[0]=1;
        fact[1]=1;

        long prod = 1;

        for(int i = 2;i <= n;i++){
            prod = (prod*i)%M;

            fact[i] = prod;
        }

        return prod;
    }

    static boolean isPrime(long n){
        for(int i = 2;i*i <= n;i++){
            if(n%i == 0)
                return false;
        }
        return true;
    }
 }

class FastReader {
    BufferedReader br;
    StringTokenizer st;

    public FastReader() {
        br = new BufferedReader(new
                InputStreamReader(System.in));
    }

    String next() {
        while (st == null || !st.hasMoreElements()) {
            try {
                st = new StringTokenizer(br.readLine());
            }
            catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

    int nextInt() {
        return Integer.parseInt(next());
    }

    long nextLong() {
        return Long.parseLong(next());
    }

    double nextDouble() {
        return Double.parseDouble(next());
    }

    String nextLine() {
        String str = "";
        try {
            str = br.readLine();
        }
        catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
}